Customer Reviews

The Calculus Wars: Newton, Leibniz, and the Greatest Mathematical Clash of All Time

5 star:		(2)
4 star:		(7)
3 star:		(2)
2 star:		(2)
1 star:		(4)

 

 

I loved this book! The author has recounted a fascinating tale about the war that ultimately ensued between Newton and Leibniz as to which one of the two was the first to discover calculus. The author complements his captivating account with highlights of the personal lives of these two individuals, as well as the pertinent politics and daily life in seventeenth and early eighteenth century Europe. The writing style is simple, friendly and quite engaging.

At first, I hesitated to buy this book, despite my love for the subject matter, because of the less than positive early reviews that it was getting. These reviews seemed to dwell mainly on the book's poor editing. Later reviews seemed more forgiving in that regard and, thus, generally more positive. So, I bought the book, read it and absolutely loved it. I do agree that the many editorial errors, although they don't occur on every page, can be rather annoying and even downright confusing at times. Such errors include word repetitions, misprints, wrong verb tenses, occasional missing words, wrong word order, bad punctuation, etc. It is for that reason alone, i.e., poor editing, that I gave it merely four stars because as far as the subject matter, the writing style and the intense interest that this book generates, it is very easily five-star material. This book should be of particular interest to math, science and history buffs alike.

As Mr. Bardi points out in his book The Calculus Wars, most modern historians of science agree that Sir Isaac Newton (the great English scientist) and Gottfried Leibniz (the great German philosopher) each discovered the calculus independently. It is also generally accepted that, though Newton discovered the calculus many years before Leibniz, Leibniz published first and continued to work on the development of the subject long after Newton had moved on to other pursuits. And therein lies a tale.

The battle between Newton and Leibniz over the "credit" for discovering calculus is one of the great intellectual priority fights in the history of science. It is fascinating for many reasons but first among these must be for the insights it provides into the personalities of two mathematical geniuses: Newton's hypersensitive and introverted nature versus Leibniz's unflinching pursuit of truth as he perceived it in the face of all obstacles. Place on top of this the fact that this fight wasn't picked until they were both in the twilight of their careers, the fact that distance and slow communication made determining what's what more difficult and the fact that, in many ways, this was a reflection of England versus the Continent and you have a war well-joined indeed.

As a physicist and teacher, I was well aware of this conflict but Mr. Bardi has done a very good job of bringing out its details. The only thing I would caution readers of is that Mr. Bardi generally stays very close to his topic. What I mean is that he only provides biographical details that are germane to his story. Being very familiar with these two characters from other reading, I was clear on most of the situations he describes. Those less familiar with the people involved may have more trouble. Still, if Newton and Leibniz are personalities that interest you, this is a lively telling of a pivotal and often lost part of their lives.

While the story of the invention of calculus is an interesting one, it would be better suited for a long, New Yorker-style article, rather than a full book. Bardi fills out the narrative with interesting, but irrelevent material, such as other projects that Newton and Leibniz developed and studied. While Bardi does a good job of capturing the personalities of Newton and Leibniz, his attempt to fill out the book with historical background information and tangential stories ultimately makes "the calculus war" itself a backburner element. If you're solely interested in the calculus side of the story, this is the wrong book for you. If you're interested in a more holistic study of Newton and Leibniz, this is a good start.

Bardi is successful, however, at reproducing the era. His chronological narrative gives good insight to the way science and scientific societies progressed in the late 17th century. His details about the circulation of letters and correpsondence written by Leibniz and Newton provide solid information about how information traveled in those days. The side stories about Leibniz' time-sapping historical projects (which he did for money) and Newton's boredom with his duties as the head of the British Mint, also demonstrate the difficult lives that even major scientists and thinkers led back in those days.

While the book's writing style is amateurish at times (Bardi likes to use exclamation points and intermittent first-person commentary and opinion, which read like office emails, rather than historical analysis), Bardi does a good job at distilling the information into a text lay-people can understand.

This book was published by a small press and accordingly has numerous typos and some grammatical errors, which were annoying, even if expected.

Students of mathematics at the calculus level and beyond are usually made vaguely aware that, despite some minor historical contention, Isaac Newton is credited for the discovery of calculus. Fewer in number are those who learn the name Gottfried Wilhelm Liebniz as Newton's rival claimant for that honor, and still fewer are those who are informed that Newton's methods of fluxions and fluents were almost immediately abandoned in favor of Liebniz's differentials and his superior mathematical notation (essentially that still in use today).

Author Jason Bardi aims to correct that knowledge shortfall in THE CALCULUS WARS: NEWTON, LIEBNIZ, AND THE GREATEST MATHEMATICAL CLASH OF ALL TIME. The use of the word "wars" and the hyperbolic phrasing "greatest clash of all time" set the expectations stage for an epic battle of intellectual giants as potentially juicy as 20-year-old Evariste Galois's fatally romantic duel with pistols. The historical facts are rather less sensational, however, consisting largely of letters and journal articles (most submitted anonymously at the time) hurling nationalistic accusations, often petty or unfounded, from one side of the English Channel to the other. As a result, Mr. Bardi struggles to deliver the implicit drama: there is no critical face-off between the principals, no momentous debate (even the British Royal Society largely shrugs it off thanks to Newton's presidency of that august body), no climactic moment when the truth is laid bare.

Perhaps more disconcerting, the vast majority of Bardi's book is not about calculus at all, not about the battle over its discovery, its historical underpinnings, or its subsequent development along the lines of Liebniz's work. We never see a comparative representation of the Newtonian and Liebnizian models, their notational differences, or their intellectual geneses from the mathematical work of their predecessors (Archimedes' famous method of exhaustion, for example, receives just one passing mention). Instead, the author falls back on the more conventional approach of chronological biography, trailing the two men's parallel lives from 1642 to 1728. It could certainly be argued that their respective biographies give important background to their personalities and professional status when the "calculus wars" finally broke out in 1699 (175 pages into Bardi's 250-page book). However, Bardi writes extensively on Liebniz's silver mining schemes, invention of a leather folding chair and a new type of windmill, promotion of binary numbers, theories of planetary motion and theology, political machinations, court genealogical work, and studies of China, to name a few. Similarly with Newton, it is his optics, theories of universal gravitation, stewardship of the British Mint, dabblings in alchemy, psychological mood swings, even his sexual orientation.

In the end, Bardi sides with Liebniz as the more aggrieved party, clearly innocent of the charges of plagiarism. Newton is clearly the loser in this "war," both for hoarding his great discovery to the detriment of fellow scientists and mathematicians and for treating his Continental contemporaries with such disdain. Sadly, the entire affair did nothing to polish the honor of either man.

Bardi's storytelling prose is fluid and well suited to his task, with one significant exception. In a tale of dueling mathematical, scientific, and intellectual giants, one inserts oneself at the greatest of risks. Perhaps a Stephen Hawking could merit an occasional authorial "I" in this story, but decidedly not a Jason Bardi (despite his ostentatiously displayed middle name, Socrates, that ironically only emphasizes the disparity). Author Bardi is given to repeated, utterly trivial, and mostly parenthetical insertions of his own opinions that are presumptuous, irrelevant, and distracting: "When I was in London, I noticed..." , "...an event I like to call..." , "I get this picture when I think about it..." , "...as I recall from my encounter..." , "For my part, I can't help but wish..." , "a docent told me..." , "I examined..." , "...I have read..." , "I examined... [again]" , culminating with the irrepressible "I'm not surprised, really" and the exquisite "For me, what's really interesting... " Every one of these first person insertions should have been removed by a more exacting editorial pencil.

I approached this book hoping to discover a comparative treatment of the origins and development of Newton's and Liebniz's twin lines of calculus development, to learn how two intellectual giants of the 18th Century each separately made a conceptual mathematical leap nearly on a par with Einstein's leap to relativity. The similarities and differences in their developmental threads would surely be part and parcel of the historical argument over rights of discovery and accusations of plagiarism. Regrettably, I found instead seemingly endless pages of biographical minutiae about everything else in these two great men's lives.

If you've read the reviews that preceded this, you probably have an idea of how disastrously this book has been edited. I will add only that which hasn't been mentioned in other reviews, which is my two cents.

I must say that I only finished this book to give the author the benefit of doubt, after fuming over the many typos, disgustingly careless grammar, factual errors and irreverent first-person comments. I'm sorry to say it wasn't worth the effort.

Before sounding like a gripe, let me tell you what this book is good for. If you like reading your history as a smattering of tidbits within the confines a specific social context, in this case the lives of two prominent scientists at the turn of the 18th century, this is worth skimming over. At best, it is a slightly precocious commentary, and at worst it has the pretentions of being an analysis, with random, irrelevant and condescending first-person accounts thrown in. Worse still, in the epilogue, we are made to feel that Bardi is really modest as he claims to be embarassed by a friend's comments regarding his expertise on the subject.

There are questions that arise out of the subject matter, however, and relevant ones. The overarching one is whether the introvert inventor or the original but flambuoyant expositor gets the credit for an issue as thorny as the invention of Calculus? If this was the question Bardi set out to answer in his book, he should have realized that a chronological biographical sketch with some seemingly relevant characters thrown in would be insufficient.

There is no level of detail regarding the mathematics here. This is disdainful, and only shows how much regard even a science writer has for the subject, or was he perhaps muffled by his very competent publishers? I tend to lean away from the latter explanation because even the verbal treatment of the mathematics is shamefully cursory. A case in point is the description of the brachistochrone problem, infamous in the calculus of variations. How is one to understand the gravity (sic) of the problem if one doesn't quite follow what has led up to it? Merely mentioning that it was a Leibniz challenge is like conjuring a rabbit out of a hat.

It is one thing to avoid equations, lest the audience feel they are talked down to, but another thing altogether to use mathematical symbols for the purely decorative, as the equations in the illustrative section have done. They have no explanations, no context whatsover, provide no insight to those who are unfamiliar with Calculus, and tautological to those who are. Instead of pulling out pages from text and rendering them unreadable in fine print even the briefest description of Newton's explanation of rainbows would have sufficed. Equations could have been in the body of the text, and where relevant, at the very least.

A discussion about Calculus necessiates a discussion about the tools and the formalism, and even if Bardi wished to avoid excessive technicality, he could have done what most good science journalists do, which is to collate and quote opinions from folks who are well-versed in the mathematical subtleties.

There are a few instances when Bardi stoops from his pedestal to do just this, and those are the few slivers of salvation this book offers. At one point (page 130), he quotes a balanced review of the Pricipia, and mentions how it lauds Newton's geometry but not his physics, since Newton is to have famously declared that 'I do not invent hypothesis' [for gravity]. At another (page 207), Bardi quotes Johann Bernuolli's defense of Liebniz when he mentions that Newton didn't quite demonstrate his method of fluxions in the Principia when he had ample chance to do so, but dogmatically stuck to the geometrical style of his predecessors.

The first case was interesting because it echoes something of Edwin Hubble's attitude regarding his data for receding galaxies. He apparently refused to interpret what his data implied, even if it favoured something like the Big Bang. From a philosophical standpoint such extreme empericism must have indeed looked bizzare and rattled Leibniz in his time, as it did contemporary astronomers.

The other instance, involving Bernuolli's commentary, is somewhat more illuminating of Newton's character. It is an irony that Newton avoided his method of fluxions (perhaps embittered by Hooke's criticism) in the Principia so it would be widely understood, and Leibniz introduced the formalism of Calculus so that it would be widely used to solve a broad class of problems. While Newton's approach was to introduce his concepts of motion and gravitation using existing geometrical tools, looking backward, Leibniz's was to introduce a generic technique of solving infinitesimal problems, complete with a set of tools and it associated new symbols, moving forward. As testimony to Leibniz's approach, we still use his symbols today. In this sense, contrary to the review of the Principia from long ago, Newton was really original in his physical insight about gravitation while Leibniz had the vision to understand that the scope of Calculus was much wider, and not just restricted to gravitation.

The redemption factors are not able to salvage the book, alas. It remains balanced but shallow, and goes to show that however well a book may be researched, an interesting narrative is one where the assimilation is almost invisible, and in a way that inspires meaningful questions. To this end, even an exhaustive bibliography still remains a means, not an end.

I knew nothing about the subject and after seeing a display about the controversy at a library; I thought I would like to learn more about the subject.

It's true there are typographical errors, but as to the content, for a layman like me, I thought the book presented a great overview of the subject with many interesting tangents. In fact, while I was reading it, I made a little list of other topics I'd like to learn more about as well. I think that's a sign of a good book.

To me, the tone of the writing was similar to a good PBS documentary- comfortable and knowledgeable.

I really enjoyed this book and found it offered a great many wonderful tidbits to fill in my understanding of the issues. My most recent previous reading on Leibniz was the wonderful book "The Courtier and the Heretic," which covers Leibniz' interrelationship with Spinoza and the two books fit nicely together. It is clear from Bardi's book that there are many more wonderful possibilities out there many of which have been available for years - a book relating Huygens and Leibniz for example. Perhaps this is one of the most wonderful aspects of a book like this. It points to many sources to explore if one is interested in following up. This book clearly details how the situation got so mixed up and why it will forever remain an embarrassment to those who value the advance of reason and wish human frailties would not create so many bumps on the path.

I did not check these reviews before picking up the book and (not plagiarizing them but independently noting them myself!) found the sheer number of editorial mistakes annoying. One wants to send it back to have it corrected out of habit. These are the sorts of mistakes Word doesn't let happen. I bet I could not even reproduce many of them here without Word automatically correcting them. But I agree this seems to be the editors fault not Bardi's since even if they were Bardi's the editor should have easily caught them. But I myself have seen multiple errors magically appear in a published text that were not there in the original. Perhaps the paperback is corrected? I did not see any mention of this on Bardi's web page either.

But I have a major point to question concerning Bardi's view that Leibniz's vortex argument has been disposed of by Newton's gravity. Would not Einstein's view of the curvature of space achieve essentially the same explanation of Leibniz'? in short, though the short history following the controversy seemed to make Newton's position on gravity the winner (not as an explanation of movements) hasn't more recent history at least shown both theories useful for different purposes and therefore both correct in context?

Perhaps my understanding of this issue is wrong? After all, in the short introduction to the Principia in "On the Shoulders of Giants" edited with commentary by Stephen Hawking he seems to suggest the same thing. What gives? What happened to Relativity?

Jason Bardi wisely decided not to write a book about mathematics. Instead, "The Calculus Wars" is an informative story about a great era of mathematical discovery. We learn much not only about the primary figures, Leibniz and Newton, and their peers (such as John Wallis and Jacob Bernoulli), but also about the contemporary dilettantes and sycophants that buzzed around them, the most damaging of which were the nobility. Too often scientists and science have been used to prop the worthless ambitions of fops, even to today's Al Gore.

Bardi is quite right in noting the superiority of Leibniz's notation. He doesn't quite see that Leibniz's universal language was the beginnings of symbolic logic as developed only in the 1800's. Bardi misses one important (and debatable) point, and it is that Isaac Newton created calculus as an indispensable tool for the mathematical development of his new physics. It is the mark of his towering genius that a revolutionary new mathematics was for him simply a means to an end. For Leibniz, calculus was a form of verification that reason could triumph over everything, certainly over the vast landscape of his endeavors. Leibniz is much more the completed Renaissance man, whereas Newton is the scientist of a future that would be molded by his thoughts.

There are grammatical and typographical errors scattered throughout the book, which jar one's reading. These are clearly not Bardi's fault, rather, some numskull editor at the Avalon Publishing Group cut corners and rushed the book to print. Typical error: Bardi correctly states on page 237 that Newton died in March of 1727, but the incompetent editor didn't catch this line one paragraph later, "He was interred in the nave of Westminster Abbey on March 28, 1726...".

Despite such potholes, Bardi's book is good reading. In these days, when every Hollywood celebrity is called a "genius", it is good to reestablish the word by proper examples, such as Sir Isaac Newton and Baron Gottfried Leibniz.

I thorougly enjoyed this book. I was not aware of the history of Newton and Leibnitz, and so this was a new subject for me. I really feel that in history classes we should read books like this, because it really opens up mathematics. I am going for phD later this year, and so I am starting to review my mathematics textbooks, such as discrete mathematics and calculus. Reading about the extraordinary men that created calculus and battled over it, made calculus seem to me like a living thing, and actually I am looking forward to reviewing my calculus
textbook! On the other hand, if you aren't a science geek, this book is still a good read, because it also gives us psychological insights into two brilliant men and the time period in which they lived.

The reviewers here have several objections to this book. Yes, there are sometimes personal comments in the writing that should have been weeded out by an editor. But this only happens every few pages, and is not hard to ignore. No, the book doesn't talk much about math. Yes, the calculus dispute itself comes rather late in the book. But so what? The author does a great job of describing the lives and times of these two fascinating men. There are lots of interesting details, but all in moderation. I am neither a mathematician nor a historian, though I enjoy reading about both subjects; to me the book was well worthwhile.